What are the types of youngs module



The modulus of elasticity (also: Tensile module or Young's module, named after the English doctor and physicist Thomas Young) is a material parameter from materials technology that describes the relationship between stress and strain when a solid body is deformed with linear elastic behavior.

The modulus of elasticity is with Modulus of elasticity or as a symbol with E. abbreviated. The plural of modulus of elasticity is modulus of elasticity.

The modulus of elasticity has the unit of tension. In clear terms, the modulus of elasticity of a material is the tensile stress at which a tension rod made of this material doubles in length. (In reality, this case never occurs, doubling the length (stretching by 100%) is not a linear-elastic deformation for any material.)

The value of the modulus of elasticity is greater, the more resistance a material opposes to its deformation. A component made from a material with a high modulus of elasticity (e.g. steel) is stiff, while a component made from a material with a low modulus of elasticity (e.g. rubber) is flexible.

The modulus of elasticity is the constant of proportionality in Hooke's law. In the case of crystalline materials, the modulus of elasticity is always direction-dependent. As soon as a material has a crystallographic texture, the modulus of elasticity is anisotropic.

definition

The modulus of elasticity is defined as the slope of the graph in the stress-strain diagram with uniaxial loading within the linear elasticity range. This linear area is also called Hooke's straight line designated.

Here, σ denotes the mechanical stress (normal stress, not shear stress) and ε the elongation. The elongation is the ratio of the change in length to the original length. The unit of the modulus of elasticity is that of a stress:

E. in , in SI units: E. in (Pascal)

The modulus of elasticity is referred to as the material constant, because it and the Poisson's ratio are used to establish the law of elasticity. However, the modulus of elasticity is not constant with regard to all physical quantities. It depends on various environmental conditions such as B. temperature, humidity or the rate of deformation.

application

At ideal linear elastic material law (proportional range in the stress-strain diagram) results in the spring constant D. of a straight rod from its cross-sectional area A., its length L.0 and its modulus of elasticity E..

With the expressions for the tension and For the elongation, Hooke's law for the 1-axis stress state is obtained from the above equation

and from this the modulus of elasticity

Typical numerical values

Notes on unit conversion:

  • (One newton per square millimeter is one mega-pascal)
  • (One kilo-newton per square millimeter is one giga-pascal)

 

In the case of flat components, flows are used instead of stresses . Therefore, a thickness-related modulus of elasticity is used here, which corresponds to a stiffness. This is the size of the unit .

Relations of elastic constants

The following relationship between the shear modulus applies to a linear-elastic, isotropic materialG, the compression moduleK and the Poisson's numberμ:

Common misunderstandings

"Is the modulus of elasticity related to other material constants?"

The modulus of elasticity is often associated with other material parameters. However, this is not easy:

  • The modulus of elasticity is not strictly related to the hardness of the material
  • The modulus of elasticity is not strictly related to the yield pointR.e of the material
  • The modulus of elasticity is not strictly related to tensile strengthR.m of the material

A simple structural steel has (almost) the same modulus of elasticity as a high-alloy, high-strength stainless steel.

But there is a general trend:

  • The modulus of elasticity of a metal increases with its melting temperature.

Tungsten has a higher modulus of elasticity than iron, than copper, than aluminum, than lead.

In addition, the following applies:

  • The modulus of elasticity of krz metals is (at a comparable melting temperature) higher than that of automotive metals.

The reason for the correlation is that both the modulus of elasticity and the melting temperature of the metals are dependent on the force-distance curve of the atoms.

"Stress reduction through better material?"

When dimensioning components, there is often the opinion that a “better” material would have to reduce the stresses. The stresses only depend on the load and the geometry (force per area) and not on the material.

In some special cases (e.g. movements of swimming bodies in the swell or in the tidal range; hindered thermal expansion), stresses are not controlled by tension but by strain. In such cases, materials with a lower modulus of elasticity can lead to component stresses being reduced.

"E-modulus = stiffness"

The rigidity of a component depends on the material used and the processing, but also on the geometry of the component. For a tension rod, the stiffness is the product of the modulus of elasticity and the cross-sectional area; for a bending beam, the stiffness is the product of the modulus of elasticity and the geometrical moment of inertia. For complex geometries, it is not possible to formulate a simple expression for “stiffness”. With the help of the finite element method, these can be reproduced using individual elements and solved with an overall stiffness matrix set up for this purpose.

"Sigma = E * epsilon"

The relationship only applies to the single-axle train. In the general 2D or 3D stress state, Hooke's law must be applied in its general form - here there are several stresses in each strain term, and several strains in each stress term, e.g. .

A determination of the strain, e.g. using strain gauges or speckle interferometry, is not yet a determination of the stresses in the component.

See also

References

  1. Calculating the modulus of elasticity of glasses (in English)

Categories: Material Properties | Strength theory